a novel technique for automatic modulation classification...

e-Περιοδικό Επιζηήμης & Τεχνολογίας e-Journal of Science & Technology (e-JST)

http://e-jst.teiath.gr 17

A Novel Technique for Automatic Modulation Classification and Time-

Frequency Analysis of Digitally Modulated Signals

M. Venkata Subbarao1, Sayedu Khasim Noorbasha

2 , Jagadeesh Thati

3

1,2,3Asst. Professor, Department of ECE, Tirumala Engg. College, Narasaraopeta, A.P., India

[email protected], [email protected]

ABSTRACT

Automatic classification of analog and digital modulation signals plays an important role in

communication application such as an intelligent demodulator, interference identification and

monitoring. The automatic recognition of the modulation format of a detected signal, the intermediate

step between signal detection and demodulation, is a major task of an intelligent receiver, with various

civilian and military applications. This paper presents a new approach for automatic modulation

classification for digitally modulated signals. This method utilizes a signal representation known as the

modulation model. The modulation model provides a signal representation that is convenient for

subsequent analysis, such as estimating modulation parameters. The modulation parameters to be

estimated are the carrier frequency, modulation type, and bit rate. The modulation model is formed via

autoregressive spectrum modeling. The modulation model uses the instantaneous frequency and

bandwidth parameters as obtained from the roots of the autoregressive polynomial. This method is also

classifies accurately under low carrier to noise ratio (CNR). This paper is also presents an improved

version of S-Transform for time frequency analysis of different digitally modulated signals to observe

variations of amplitude, frequency and phase.

KEYWORDS

Instantaneous Frequency, Bandwidth, Kurtosis, Modified S-Transform

1. Introduction

The interest in modulation classification has been growing since the late eighties up

to date. Previous modulation classification systems have relied on manual

identification of signal parameters. Due to the increased activity in the frequency

spectrum, manual identification is becoming less practical and automated techniques

for modulation classification are becoming desired. Automatic modulation

classification (AMC) is an intermediate step between signal detection and

demodulation, and plays a key role in various civilian and military applications such

as signal confirmation, interference identification, monitoring, spectrum management

and surveillance. Implementation of advanced information services and systems for

military applications in a crowded electromagnetic spectrum is a challenging task for

communication engineers. Friendly signals should be securely transmitted and

received, whereas hostile signals must be located, identified and jammed. The

spectrum of these signals may range from high frequency (HF) to millimeter

frequency band, and their format can vary from simple narrowband modulations to

wideband schemes. Under such conditions, advanced techniques are required for real-

time signal interception and processing, which are vital for decisions involving

electronic warfare operations and other tactical actions. Furthermore, blind

recognition of the modulation format of the received signal is an important problem in

commercial systems, especially in software defined radio (SDR), which copes with

the variety of communication systems. Usually, supplementary information is

transmitted to reconfigure the SDR system. Blind techniques can be used with an

intelligent receiver, yielding an increase in the transmission efficiency by reducing the

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18

overhead. Such applications have emerged the need for flexible intelligent

communication systems, where the automatic recognition of the modulation of a

detected signal is a major task.

A simplified block diagram of the system model is shown in Figure 1. The design

of a modulation classifier essentially involves two steps: signal preprocessing and

proper selection of the classification algorithm. Preprocessing tasks may include, but

not limited to perform some or all of, noise reduction, estimation of carrier frequency,

symbol period, and signal power, equalization, etc. Depending on the classification

algorithm chosen in the second step, preprocessing tasks with different levels of

accuracy are required; some classification methods require precise estimates, whereas

others are less sensitive to the unknown parameters.

Signal interception consists of signal detection followed by estimation of

modulation parameters and finally demodulation. A signal of interest (SOI) is

generally detected by a spectrum receiver. The frequency band of interest is then

further processed to estimate modulation parameters. The modulation parameters

considered are the carrier frequency, modulation type and bit rate. The modulation

types that are considered are Continuous Wave (CW), Phase Shift Keying (PSK),

Frequency Shift Keying (FSK), Amplitude Shift Keying (ASK) and Quadrature

Amplitude Modulation (QAM).

Figure 1. Simplified block diagram

Several methods have been suggested for estimating modulation parameters, i.e. by

using statistical moments [2], zero crossing rates [3], and analytical signal

representations [4]. This paper uses a modulation model as formed by autoregressive

spectrum modeling. The new model allows for an efficient, robust method of

estimating modulation parameters.

This paper presents a new method for modulation classification. The following

section provides the formulation, which includes a description of the modulation

model in addition to its formulation via autoregressive spectrum modeling. The

classification algorithm is then described and a flowchart is provided. This section is

followed by computer simulation results and the conclusion of this paper.

2. Mathematical Model

This paper utilizes a signal representation known as the modulation model to aid in

estimating modulation parameters. The modulation model represents a

multicomponent signal as a sum of single component signals in terms of their

Modulat

or

Channel + + Preproces

sor Demodulat

or

Classificati

on

algorithm

Input

symbols

Interference

jamming Receiver

Noise

Modulation

Format

Estimated

Input

symbols



individual amplitude modulation (AM) and phase modulation (PM) [5]

))(cos()()(1

tttAty ii

n

i

i

(1)

where i denotes the component, Ai(t) is the signal envelope (AM), and Φi(t) is the instantaneous

phase (PM). This parameter only considers constant envelope signals, so the Ai(t) term will be

replaced by A in subsequent analysis. Since the frequency band of interest is assumed to contain one

SOI, the parameter n in equation (1) will be equal to one.

The signals that are considered are CW, Binary Phase Shift Keying (BPSK), Quadrature Phase Shift

Keying (QPSK), Frequency Shift Keying (FSK), Amplitude Shift Keying (ASK) and Quadrature

Amplitude Modulation (QAM). The modulation model for a discrete signal within these categories

will appear as

))(cos()( kkAky c (2)

where ωc is the carrier frequency, θ is the phase at the receiver and

QFSKkk

BFSKk

QPSK

BPSK

CW

k

dd

d

,2

,2

,0

,0

0

)( (3)

In the above equation, the ωd represents the frequency deviation for the FSK modulation type.

The modulation model considered here is formed by estimating the instantaneous

frequency of the desired signal, which is computed using autoregressive spectrum

analysis. Autoregressive spectrum estimation is an alternative to Fourier analysis for

obtaining the frequency spectrum of a signal. The method used here for autoregressive

spectrum analysis consists of estimating the autocorrelation coefficients followed by

an inversion of the autocorrelation matrix. Given an input signal:

)()()( knkykx (4)

Autoregressive spectrum modeling can be accomplished by solving the following

system of equations:

Rxx(0) Rxx(1) ………. Rxx(N-1) 1a Rxx(1)

Rxx(1) Rxx(0) ……… Rxx(N-2) 2a Rxx(2) . .

. . = . (5) . . . . .

Rxx(N-1) Rxx(N-2) ……… Rxx(0) na Rxx(N)

where the autocorrelation estimates Rxx(k) are found as:


(5), 7, 2012 20

20

)()()(ˆ

0

knxnxkRM

n

xx

(6)

The M in the equation (6) represents the number of samples in the analysis frame. In equation

(5), the a vector represents the coefficients for the polynomial that best fits the frequency spectrum.

The Z-domain expression for this polynomial is:

N

N ZaZaZa ....1 2

2

1

1

The roots of this polynomial are related to the spectral peaks and their corresponding

bandwidths. This relation is illustrated in Figure 2.

In Figure 2, the angle and magnitude terms, i and Mi respectively, correspond to

the frequency and bandwidth for the pole Zi. The exact result can be obtained from

the following equations:

)]Re(/)[Im(tan)2/().2/( 1

iisisi ZZFFF (7)

The quantity Fi provides measure for the Average frequency within the analysis

frame. At this point, if the signal is classified as (PSK, CW) sub class, to classify

whether the signal is PSK or CW, „Standard Deviation over Instantaneous frequency‟

of the signal is used. Because, in case of PSK, a phase change in time domain

corresponds to sudden change of frequency in frequency domain. Where as in CW

signal there is no phase change as well as frequency change. Therefore „Standard

Deviation over Instantaneous frequency‟ of PSK is slightly higher than for CW signal.

Figure 2. Pole–Frequency relation

Hence, by putting a threshold, incoming signal can be classified as PSK or CW. If

the signal is classified as PSK, then it should be further classified as BPSK or QPSK.

Higher order statistics are used to classify whether the signal is BPSK or QPSK.

3. Classification Algorithm

3.1 Basic steps: The algorithm for performing modulation classification is given by the following

steps.

1. The unknown modulated signal‟s Instantaneous parameters such as

Instantaneous frequency and bandwidth are measured using appropriate

transformations (autoregressive spectrum modeling).



2. In the first step of classification, kurtosis value is calculated on a given set of

samples (typically 4096 samples will be taken for analysis). The kurtosis value

will be proportional to amount of amplitude variations.

3. Hence the kurtosis value will be more for amplitude modulated signals and

less for frequency and phase modulated signals. So based on a specific

threshold value, the signal will be classified as either amplitude modulated

(ASK, QAM) or angle modulated (PSK, FSK).

4. If the signal is angle modulated type, then the standard deviation among the

instantaneous frequency array is calculated and compared with threshold value

to decide whether the signal is PSK or FSK.

5. Since FSK signals will have more abrupt frequency variations when compared

to PSK signals, if the standard deviation is above threshold it is classified as

FSK type otherwise it is PSK type.

6. If the signal is PSK type, then to find whether it is BPSK or QPSK, frequency

domain techniques will be used.

7. The instantaneous amplitude of the signal is squared and for the resulting

values, FFT (Fast Fourier Transform) is calculated.

8. If the FFT consists of only a narrow peak, then it is a BPSK signal. If the FFT

comes in bell shaped wide curve with multiple peaks then it will be classified

as QPSK.

9. Incase if the signal is classified as amplitude modulated type (in step 3), then

further thresholds are applied on kurtosis value and standard deviation to

classify either as ASK or QAM. The kurtosis value will be higher for ASK

signals when compared to QAM signals.

3.2 Higher order statistics

3.2.1 Kurtosis

In probability theory and statistics, kurtosis is a measure of the “peakedness” of the

probability distribution of a real-valued random variable. Higher kurtosis means more

of the variance is due to infrequent extreme deviations, as opposed to frequent

modestly-sized deviations.

The fourth standardized moment is defined as μ4 / σ4, where μ4 is the fourth

moment about the mean and σ is the standard deviation. This is sometimes used as the

definition of kurtosis in older works, but is not the definition used here. Kurtosis is

more commonly defined as the fourth cumulant divided by the square of the variance

of the probability distribution,

34

4

2

2

42

k

k

which is known as “excess kurtosis”. The "minus 3" at the end of this formula is often

explained as a correction to make the kurtosis of the normal distribution equal to zero.

3.2.2 Standard deviation

In probability and statistics, the standard deviation of a probability distribution,

random variable, or population or multi set of values is a measure of the spread of its

values. It is defined as the square root of the variance. The standard deviation is the

root mean square (RMS) deviation of values from their arithmetic mean. For example,


(5), 7, 2012 22

22

in the population {4, 8}, the mean is 6 and the standard deviation is 2. This may be

written: {4, 8} ≈ 6±2. In this case 100% of the values in the population are at one

standard deviation of the mean.

The standard deviation of a random variable X is defined as:

)))((( 2XEXE = 22 ))(()( XEXE

where E(X) is the expected value of X.

3.3 Flow chart for modulation classification

Figure 3. Flow chart for modulation classification

3.4 Classification between (ASK, QAM) / (PSK, FSK, CW) classes

Kurtosis is a measure of how outlier-prone a distribution is. The kurtosis of the normal

distribution is 3. Distributions that are more outlier-prone than the normal distribution have kurtosis

greater than 3; distributions that are less outlier-prone have kurtosis less than 3. The kurtosis of a

distribution is defined as

Kurtosis of a given signal element =4

4)(

XE

Where µ is the mean of x, Σ is the standard deviation of x, and E(t) represents the expected value of

the quantity t. Therefore, as ASK and QAM signals have amplitude differences in their envelopes

the value of Kurtosis will be more than for PSK,FSK,CW class of signals where the envelope is

constant. Hence, by putting a suitable threshold the incoming unknown signal will be classified into

(ASK, QAM) / (PSK, FSK, CW) classes.

If the incoming unknown signal is classified into (PSK, FSK, CW) class, it should be further

classified into PSK or FSK or CW.



3.5 Classification between PSK, FSK, CW

The statistical parameter used to classify these modulations is Standard Deviation over

Instantaneous Frequency. In FSK, the frequency of modulated signal will change continuously

between Mark frequency and Space frequency depending upon the data randomness. Therefore, the

instantaneous frequency of FSK will vary continuously. And, hence „Standard Deviation over

Instantaneous frequency‟ of FSK is more compared to PSK, CW signals where there won‟t be any

frequency change in the signal. By putting a suitable threshold, incoming signal classified as FSK /

PSK, CW sub classes.

3.6 Classification between BPSK/QPSK

Higher order statistics means raising the signal to second power, fourth power, eighth power etc. If

the incoming signal is BPSK, raising the signal to second power yields CW signal i.e., modulation

of the signal is removed. Because BPSK has only one phase difference which is 180 degrees. After

squaring BPSK signal, 180 degree phase difference will become 0 degree phase difference.

Therefore, signal lost phase information and became a CW signal. But, if the unknown incoming

signal is QPSK, raising the signal to second power does not yield a CW signal. Because, QPSK has

3 phase differences called 90, 180, 270 degrees. Raising the QPSK signal to second power doesn‟t

cause total loss of phase information. It still contains some phase information. Therefore spectrum

of squared BPSK will contain only one peak at 2fc frequency. Where fc is frequency of carrier. But

spectrum of squared QPSK will look like a bell shaped one. Hence, variance over spectral data of

squared BPSK is far less compared to variance over spectral data of squared QPSK. By putting a

suitable threshold over variance of squared signal‟s spectral data, unknown signal will be classified

as BPSK or QPSK.

3.7 Classification between ASK and QAM:

QAM signal will contain both phase and amplitude changes during symbol transition. But ASK will

contain only amplitude changes. Therefore Instantaneous frequency of QAM is higher compared to

instantaneous frequency of ASK. Consequently Standard Deviation over Instantaneous frequency

will be higher for QAM than for ASK. Hence, by putting a threshold over Instantaneous frequency,

incoming signal can be classified as ASK or QAM.

4. Improved S-Transform

The ST of a time series tx is defined as [1]:

deftwxfts fi2,),(

(8)

=

deef

x fif

t

2)(2

)(2

2

2)(

1

The standard deviation σ (f) of the window w of the standard S-transform in equation (8) is

ff /1)( (9)

For the modified Gaussian window, we have chosen the standard deviation )( f to be

)//()( fbakf (10)

Where ba, are positive constants, f = signal fundamental frequency and 22 bak . In equation

(1), the usually chosen window w is the Gaussian one. Thus, the spread of the original Gaussian

function is being varied with frequency to generate the new modified Gaussian window as

0,

2,

22

22)(

kek

fbaftw k

tfba

(11)

In which f is the frequency, t and the time variables and k, b are scaling factors that control the

number of oscillations in the window; a is a constant. When k is increased, the window broadens in


(5), 7, 2012 24

24

the time domain and hence frequency resolution is increased in the frequency domain. Again by

setting b=0 and k=1 we can obtain the Short -Time Fourier Transform explicitly. Thus, an

alternative representation for the Generalized S- transform with modified Gaussian window is

deefXfS ifbaK 2

2)()2( 222

,

(12)

The discrete version of the S-Transform of a signal is obtained as

N

mjifbaKm

N

m

eenmXnjS

2)/(2(

1

0

2222

],[

(13)

5. Simulation Results

The algorithms outlined in the previous sections were tested with MATLAB software. The

simulation consisted of a carrier frequency of 25 KHz, whose bit rate or symbol rate is 5

KHz, received through AWGN channel of SNR 15db.The sampling rate was 125

KHz. The time frequency contours using modified S-transform are shown in Figures 4 to 9.

Modified S-transform provides excellent detection, visual localization of variations in the

modulated signals i.e. amplitude, frequency and phase.

Figures 4-9 show the time-frequency contours of different digitally modulated signals with

modified S-transform, and these contours clearly show the nature of modulation is presence. For

example figure 5. (a) represents the input un-modulated digital signal, (b) shows the BPSK

modulated signal, (c) represents the normalized time-frequency contour of the BPSK modulated

signal. In this we can observe that there is no change in the frequency but at where the phase of the

carrier is changed, it tracks that location and by visually shows which type of modulation is present.

(d) represents the magnitude-time spectrum obtained by searching rows of ST matrix. Figures

6-9 (a)-(d) show similar plots as in Fig. 4 and 5 obtained from ST analysis.

Instantaneous frequency and standard deviation of different digital modulation techniques are

tabulated is shown in Table 1. These parameters are used to classify different digital modulation

techniques.

0 20 40 60 80 100 120 140 160 180 200-1

-0.5

0

0.5

1 INPUT DATA

...........> Time samples

Ampli

tude

0 20 40 60 80 100 120 140 160 180 200-2

-1

0

1

2 CONTINUOUS WAVE


Ampli

tude

Norm

alize

d Fr

eq.

(b) Sample Points

Time-Frequency Countour

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120 140 160 180 2001.3

1.35

1.4

1.45

1.5

1.55

Mag

nitud

e

(c) Sample Points

Figure 4. Continuous Signal (no modulation)



0 20 40 60 80 100 120 140 160 180 200-1

-0.5

0

0.5

1 INPUT DATA


Ampli

tude

0 20 40 60 80 100 120 140 160 180 200-2

-1

0

1

2 CONTINUOUS WAVE


Ampli

tude

Norm

aliz

ed F

req.

(b) Sample Points


0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120 140 160 180 2000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Mag

nitu

de

(c) Sample Points

Figure 5. BPSK modulated signal

0 20 40 60 80 100 120 140 160 180 200-1

-0.5

0

0.5

1 INPUT DATA


Ampl

itude

0 20 40 60 80 100 120 140 160 180 200-2

-1

0

1

2 CONTINUOUS WAVE


Ampl

itude

Norm

alize

d Fr

eq.

(b) Sample Points


0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120 140 160 180 2000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Mag

nitud

e

(c) Sample Points

Figure 6. QPSK modulated signal


(5), 7, 2012 26

26

0 20 40 60 80 100 120 140 160 180 200-1

-0.5

0

0.5

1 INPUT DATA


Ampl

itude

0 20 40 60 80 100 120 140 160 180 200-2

-1

0

1

2 CONTINUOUS WAVE


Ampl

itude

Norm

alize

d Freq

.

(b) Sample Points


0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120 140 160 180 200

0.8

1

1.2

1.4

1.6

Magn

itude

(c) Sample Points

Figure 7. FSK modulated signal

0 20 40 60 80 100 120 140 160 180 200-1

-0.5

0

0.5

1 INPUT DATA


Ampli

tude

0 20 40 60 80 100 120 140 160 180 200-3

-2

-1

0

1

2

3

4 CONTINUOUS WAVE


Ampli

tude

Nor

mal

ized

Fre

q.

(b) Sample Points


0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120 140 160 180 2001

1.5

2

2.5

3

Mag

nitu

de

(c) Sample Points

Figure 8. QAM modulated signal



0 20 40 60 80 100 120 140 160 180 200-1

-0.5

0

0.5

1 INPUT DATA


Ampl

itude

0 20 40 60 80 100 120 140 160 180 200-4

-2

0

2

4 CONTINUOUS WAVE


Ampl

itude

Norm

alize

d Fr

eq.

(b) Sample Points


0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120 140 160 180 2001

1.5

2

2.5

3

Mag

nitud

e

(c) Sample Points

Figure 9. ASK modulated signal

Table 1. Modulation parameters of different Modulation techniques

S.NO. Modulation Technique Instantaneous

Frequency(10^4)

Standard Deviation

1 CW 2.79 0.00057

2 BPSK 2.78 0.00180

3 QPSK 2.80 0.00250

4 FSK 2.62 0.08950

5 ASK 2.792 0.00074

6 QAM 2.791 0.00290

6. Conclusion

A new method has been presented for modulation classification of digitally modulated

signals. This method uses a modulation model representation of a signal to provide a

convenient from for subsequent analysis. The modulation model is formed by

estimating the instantaneous frequency and bandwidth using autoregressive spectrum

analysis. The new method performed extremely well for input CNRs as low as 15 dB.

The S- transform with modified Gaussian window is used in this paper as a powerful

analysis tool for detection, visual localization of variations in the digitally modulated

non-stationary signal waveforms.

7. References

[1] H.C.Lin,”Intelligent Neural Network-based fast power system harmonic

detection”, IEEE Transactions on Industrial Electronics, vol.54, no.1, pp.43-

53, 2007.


(5), 7, 2012 28

28

[2] J.E Hipp, “Modulation classification based on statistical moments”, IEEE

MILCOM 1986 conference proceedings, Montery, Ca, Oct 1986.

[3] S.Hsue and S. Soliman, “Automatic modulation recognition of digitally

modulated signals”, In IEEE MILCOM 1989 conference proceedings, 1989.

[4] J.Mammone, R.J.Rothaker, and C.I.Podilchuck, “Estimation of carrier

frequency, modulationtype and bit rate of an unknown modulated signal”, In

proceedings IEEE International conference on communications, seattle, Wa.,

June 1987.

[5] K.T Assaleh and R.J. Mammone, “Spectral temporal decomposition of multi-

component signals”, to appear in sixth IEEE SP Workshop on Statistical signal

and Array Processing, Victoria, Oct-1992.

Authors Profile

M. Venkata Subbarao received his M.Tech degree from JNTU Kakinada, India in

2011. Present he is working as a Assistant Professor, Department of Electronics and

Communication Engineering in Tirumala Engineering College, Guntur, A.P, India.

His current areas of research interests include Signal Processing, Communication

systems and Pattern Classification.

N.Sayedu khasim received his M.Tech degree from ANU, A,P, India in 2010.

Presently he is working as a Assistant professor, Department of Electronics and

Communication Engineering in Tirumala Engineering College, Guntur, A.P, India.

His current areas of research interests include Communication and Radar

systems,Digital signal processing.

Jagadeesh Thati received the M.Tech. in DSP from JNTU Hyderabad and M.Sc.

from the Department of Electrical Engineering, BTH, Sweden, in 2009 and 2010,

respectively. From 2008 to 2010, he was a Researcher at Dasa Control systems, Vaxjo

University and BTH. He is currently working as a Assistant professor, Department of

ECE in Tirumala Engineering College Guntur. His current research interests include 2-

D/3-D digital image processing, robotics, and contents security.

a novel technique for automatic modulation classification...

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